OFFSET
1,2
COMMENTS
Differences |a(i)-a(j)| are prime powers for all i,j. Conjecture: sequence is bounded.
Proof that sequence is complete: Assume there is some k after the term 12. Then {k-1, k-3, k-5} must contain a multiple of 3. Also {k-8,k-10,k-12} also contains a multiple of 3. No prime > 12 is a multiple of 3, so the multiples of 3 are both prime powers. This implies there must be two powers of 3 that have a difference at most 11, but no such pair exists > 12 (only 1,3 and 3,9 qualify.) - Jim Nastos, Aug 09 2002
There is an elementary proof that no set of seven integers of this kind exists. - Don Reble, Aug 10 2002
EXAMPLE
a(5) = 10 as 10-8, 10-5, 10-3, 10-1 or 2, 5, 7, 9 are prime powers.
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Amarnath Murthy, Aug 04 2002
EXTENSIONS
Sixth term from Jim Nastos, Aug 09 2002
STATUS
approved